Capillary Waves

Jenny Novak
A technique used to generate small droplet size
Used two different ways, one is where you pour
water over the ultrasonic transducer, the second
is you vibrate a tube to create the droplet size
Medical Field (vapor inhalation)
Commercial Humidifiers
Fog machine
Agricultural equipment??
Nebulizer (Used for
Waves that have a boundary between two
fluids. In this case its air and water.
Dynamics are mainly due to surface tension.
(Like the string, when it has a high tension we
see a higher frequency, with lower tension,
lower frequency.)
The sound waves
from the transducer
excite the water
waves until small
droplets break off
This relates wave frequency to wave
propagation speed. (λ=v/f)
k= 2π/λ
ω= angular frequency (2pi*f)
σ= surface tension coefficient
ρ= density of the heavier fluid
ρ’= density of the lighter fluid
*my experiments will only contain
one fluid so I can get rid of ρ’
From Rayleigh’s “The Theory of Sound”
We start with assuming the forces are conservative
and use Newton’s laws, and obtain equations of
From the fact that there is no flux in or out we can
use Gauss Divergence equation and show that the
velocity potential is equal to zero.
Want the velocity potential equal to zero so we can
solve for the velocity, and relate it to frequency.
Bring in a pressure equation, which is where we
can bring the tension and density into the
Uses sound waves to produce droplets
Dispersion relation is how we can get the wave
frequency to wave propagation speed
From the dispersion relation we can obtain
Rayleigh’s equation, Kelvin’s equation and
Lang’s relation which relates droplet diameter
to frequency.
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